Finding Points on circles


I’m trying to calculate the length of a belt that will wrap around a series of pulleys. I’m doing it by hand right now but I’m sure there’s a better way to do it. Any tips? Here’s a simple example. the red line is the one I’m trying to find.
Example.3dm (2.2 MB)


DimCurveLength should do the trick. Or would you like to calculate the length before drawing e.g. to use a belt with given length?

Well, you could Split the circles with the lines, then Join the appropriate segments into your “belt” then use the Length command to get the length… Afterwards Undo back to the unsplit condition if needed.

I should add that if you are doing this repeatedly, Grasshopper would be ideal to be able to modify your geometry - circle diameter/location, line end points etc. - and get your length real-time.


Sorry I wasn’t clear. I’m trying to find the points on the two circles where a line would intersect. I’m not sure what that point is called. So where a belt stretched between those pulleys would fit

I guess you mean the tangent points. Command “Line”, select option “Tangent” (shortkey t), select option “2Curves” (shortkey c), and click on the two circles about where you want the line to touch those.


I thought you used the tangent to 2Curves command, if you found these points on the circles in the file manually: respect!

Tangent! yes that’s exactly what I was looking for. I know I should have payed more attention in geometry. I guess the plus side is I got really good at eyeballing it.